Research On The Batching Decision Problem With Uncertainty On Unfulfilled Quantity Of Order By A Robust Optimization Approach

Batching decision in steelmaking and continuous-casting production plays an important role to improve facilities utilization and production efficiency and to reduce material loss and energy consumption.The complex process of iron and steel production leads to the poor stability of the product quality.This makes the work-in-process products(slabs and coils)often associated with or decoupled from orders arbitrarily.Therefore,the unfulfilled quantity of the order in the steelmaking process is uncertain.From the perspective of robust optimization,this thesis studies the one-level and double-level batching problems involved in the steelmaking-continuous casting production.The purpose is to obtain stable batching schemes under various scenarios of unfulfilled quantity parameters so as to meet the requirements on precision feeding and improving the ability to resist interference for production process.The main contents of this thesis are as follows:1)In view of the fact that there is an increase of unfulfilled quantity due to material quality and a decrease of unfulfilled quantity due to the match of the surplus materials to unfulfilled orders,we study a one-level batching decision with uncertainty on unfulfilled quantities of orders.The "box" is used to describe the set of uncertainty on unfulfilled quantity.By considering the production constraints such as the capacity limit on steelmaking furnace,the substitution relationship between different steel grades,the requirement on identical casting width for different orders within a batch,we formulate the problem as a two-stage robust optimization model with the objective of minimizing the inventory costs of surplus slabs,profit loss due to using slabs of a higher level steel grades to fulfill the orders of lower level steel grades,and delay penalty to the orders that is unfulfilled at the current planning horizon.For the two-stage robust optimization model,the first stage decides the number of charges for each batch corresponding to a given combination of steel grade and width,and the second stage decides how to allocate the orders to batches designed at the first stage.2)The traditional management mode for batching decisions is to batch orders into charges first,and then batch charges into casts.Such sequential method may lead to the difficulty to batch some isolated charges with other charges.To overcome such difficulty,we study a double-level batching problem in which the decision of batching orders into charges and the decision of batching charges into casts are integrated.By taking the charges having the same steel grade and width as a node,and the connection relationship between each pair of charges as an arc,we develop a network to represent to problem.Based on the network representation and considering the uncertainty of the unfulfilled quantity,we formulate the two-level batch planning problem as a robust optimization model in which the decisions include the assignment of orders to nodes and paths selection.Based on the analysis of the decision variables' characteristics,the model is decomposed into an integer programming master problem and a bilinear programming slave problem.3)To solve the robust optimization models of one-level and double-level batching problems,a Benders decomposition algorithm is proposed to decompose the original model as an integer programming master problem for the first-stage decision and a slave problem for the second-stage decision whose dual is a bilinear programming model,and then the master problem and the slave problem are iteratively solved until the dual gap achieves the predefined precision.For the master problem,the valid inequality is proposed to tighten the lower bound.For the slave problem,it is firstly transformed into a mixed integer programming model by replacing the bilinear term of the objective function as a set of auxiliary variables,and then is exactly solved by the CPLEX optimization solver.To speed up the overall convergence of the algorithm,an outer approximation algorithm is also proposed to solve the slave problem approximately.Finally,the outer approximation algorithm is combined with the exact algorithm to solve the slave problem such that the solution procedure is accelerated and meanwhile the accuracy of the solution is guaranteed.The effectiveness of the proposed model and algorithm is verified by a set of numerical experiments.